What do you call a measurement that's halfway between ordinal and interval? Suppose you have a measurement $Y_i$.  Now suppose that the differences between two measurements $\delta_{ij}=Y_i-Y_j$ are an ordinal measurement.  From my understanding, $Y_i$ is more informative than an ordinal measure because the differences are meaningful.  But it also is less informative than an interval scale because the intervals are not a ratio measurement.
What do you call $Y_i$?
An example that I was thinking of is a points system for a ladder in a sporting competition.  Suppose the top three teams in some sport have $72,60,58$ points respectively at the end of a season.  Then I would expect the first team to be "better" than the second team by a larger amount than the second team is "better" than the third team as $(72-60)>(60-58)$.  But I wouldn't say that they are $6$ times "better" ($6=\frac{72-60}{60-58}$) using this measurement - I would just say (using poor grammar) "more better".
 A: Stevens' classification scheme can be useful, but it is by no means complete nor perfect. I wrote about this on Yahoo Voices.
Using Stevens' scheme you can only call your variable ordinal, since he doesn't a name for what you've got. I don't know of any particular name for a variable like yours. I propose "semi-interval" :-)
By the way, an interval level variable does not have to have ratio equivalence (that would be ratio scale), it has to have arithmetic equivalence. For example, temperature in degrees F or C is not ratio scale (50 degrees is not "twice as hot" as 25) but the difference between 50 and 25 is, in some sense, the same as that between 25 and 0. 
A: Would you regard (72-60) = (60-48) = (48-36)? 
That would imply (72 - 48) = 2 * (48 - 36) which you don't want to accept.
You "expect"/would say that (72-60) > (60-58) implying some unstated quantification of the differences. I guess you would accept that (72-72) < (60-58). For what value of x would you say, at least approximately, that (72-x) = (60-58)?
If you can be explicit about your quantification of differences you can re-scale to a conventional interval scale. Otherwise I think your unstated, subjective, assessment of the relative magnitude of differences is not very useful, and your scale is no more than ordinal.
